According to witnesses, 35-year-old Tan Do pulled out a gun -- just after the party had sang "Happy Birthday" -- and ushered the children out of the way before firing on 29-year-old Trini Do and her family. Five people died and four others were wounded before Do shot and killed himself.

Tan Do, 35, and Trini Do, 29, were hosting the party at the Roller World Skating Rink in the Dallas suburb of Grand Prairie, Texas, on Saturday for one of their two children, Grand Prairie police said in a statement.

"The couple had been involved in ongoing marital problems and it is believed that this led to the shooting," police said. "Trini Do was among the deceased."

Police responded to a call of a shooting at 7:10 p.m. Saturday (8:10 p.m. ET). Officers found the bodies of five people; a sixth person -- the suspect -- with a gunshot wound to the head; and four other people who had sustained non-life-threatening injuries.

Others who were killed included Trini Do's sisters, Lynn Ta, 16, and Michelle Ta, 28; her brother, Hien Ta, 21; and her sister-in-law, Thuy Nguyen, 25. "It appears the suspect targeted his estranged wife and her family members," police said.